The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  X  1  1  1  1 X^3  1  1  1  1  1  1  1  1 X^2  1  X  1  0 X^3  1  X X^3 X^3+X^2  0  1  1  X  1
 0  X  0  X  0 X^3 X^3+X  X X^2 X^2+X X^2 X^2+X X^2 X^3+X^2+X X^3+X^2 X^2+X X^2 X^3+X^2+X X^3 X^2+X X^3+X  X X^2+X  0 X^3+X^2 X^2 X^3+X X^3+X X^3+X X^2 X^2 X^3 X^3+X X^2 X^3+X^2 X^3+X^2 X^2+X X^3+X^2  X  X X^3+X X^2  X X^2 X^3+X^2+X X^3+X^2+X  X  X X^3+X^2  X  X  X  X X^2 X^3 X^2+X X^2+X
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^2 X^2 X^3+X^2+X  X  0 X^3 X^3+X X^2+X X^3+X^2  X  0 X^2+X X^2 X^3+X X^3+X  X  0 X^3 X^3+X^2+X X^2+X X^3+X^2 X^3+X^2+X  X X^3+X^2+X X^3+X^2 X^3+X  X  0 X^2+X X^2+X X^3  0 X^2+X X^3 X^2+X X^3+X^2 X^3+X^2 X^2 X^3+X^2+X  0 X^2 X^3+X^2 X^2 X^3+X X^3+X X^3  0 X^3+X X^3+X X^3+X
 0  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+152x^52+180x^53+430x^54+468x^55+688x^56+588x^57+502x^58+384x^59+319x^60+108x^61+114x^62+36x^63+70x^64+20x^65+26x^66+8x^67+1x^68+1x^88

The gray image is a linear code over GF(2) with n=456, k=12 and d=208.
This code was found by Heurico 1.16 in 0.391 seconds.